A Performance Comparison of Density-of-States Methods (Communications in Computational Physics, 2018)
Nowadays equilibrium thermodynamic properties of materials can be obtained very efficiently by numerical simulations. If the properties are needed over arange of temperatures it is highly efficient to determine the density of states first. Forthis purpose histogram- and matrix-based methods have been developed. Here wepresent a performance comparison of a number of those algorithms. The comparisonis based on three different benchmarks, which cover systems with discrete and continuous state spaces. For the benchmarks the exact density of states is known, for onebenchmark – the FAB system – the exact infinite temperature transition matrix Q is alsoknown. In particular the Wang-Landau algorithm in its standard and 1/t variant arecompared to Q-methods, where estimates of the infinite temperature transition matrixare obtained by random walks with different acceptance criteria. Overall the Q-matrixmethods perform better or at least as good as the histogram methods. In addition, different methods to obtain the density of states from the Q-matrix and their efficienciesare presented.
Keywords: Histogram-based density of states methods; Matrix-based density of states methods; Wang-Landau algorithm; parQ algorithm; TMMC.